Although the BBC chairman's appointment is made formally by the Queen, it is done in practice by the prime minister on the advice of the Department for Culture, Media and Sport.

Lyons's successor will be recruited under the Nolan rules for public appointments. When he was appointed in 2007 a panel chaired by a civil servant shortlisted four candidates. Ministers were then able to add another name to the list before all five were interviewed by the panel.

The panel then put forward four of the five for potential appointment, recommending one more highly than the others.

Parry has been an adviser to the culture secretary, Jeremy Hunt, on how to encourage commercially viable local television networks and attended his first public speech after he was appointed culture secretary. For some months there has been speculation that he is in line for a plum job at the BBC.

A former chairman of regional newspaper group Johnston Press, his other media experience includes being chief executive of advertising, radio broadcasting and live entertainment giant Clear Channel International before the live business was spun off in 2005.

Hodgson by contrast has spent years at the BBC. She joined the corporation as a member of the founding team of the Open University and became its influential director of policy and planning under former director general John Birt in the 1990s.

Principal of Newnham College Cambridge, she is said to be "robust" in some of her discussions with Lyons during trustee meetings.

She began her career in the Conservative Research Department and stood as a Tory candidate in 1974 but has previously insisted she is not "a party person" and that her links to the party ended in the early 1980s.

Hodgson was described in her former boss John Birt's memoirs as an "extraordinarily smart operator" and has the advantage that she already has experience of working within the BBC and the trust.

Her other experience includes three years as chief executive of now defunct commercial TV regulator, the Independent Television Commission, which she joined after she left the BBC in 2000.